GATE_PROJ
Top 16 Positive Activations
Rollout 0, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 1, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 2, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 3, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 4, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 11, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 6, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 7, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 8, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 9, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 10, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 16, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 12, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 13, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 14, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Rollout 15, Act: 0.012
<|im_start|>systemĊYouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>user
Top 16 Negative Activations
Rollout 21, Act: -6.294
âĨĴZĠwithĠsuchĠregularityĠ(likeĠsatisfyingĠadditivityĠandĠcertainĠfunctionalĠequations)ĠmightĠhaveĠtoĠbeĠconstant
Rollout 49, Act: -6.295
ĠhasĠcountableĠspreadĠandĠisĠT5Ġ(hereditaryĠnormal),ĠwhichĠweĠmightĠorĠmightĠnotĠhave,
Rollout 46, Act: -6.298
ĠwithĠangularĠvelocityĠÏī.ĠTheĠaccelerationĠinĠtheĠinertialĠframeĠisĠa_inertialĠ=Ġa_rot
Rollout 21, Act: -6.300
ĠtheĠimageĠisĠtheĠentireĠsetĠZ.ĠSoĠsurjectiveĠontoĠZ.ĠSoĠfunctionsĠinĠXĠareĠsurjective
Rollout 46, Act: -6.307
,ĠwhichĠareĠusuallyĠpartĠofĠtheĠpotentialĠinĠanĠinertialĠframe.ĠTheĠlastĠtermĠisĠsimilarĠtoĠa
Rollout 81, Act: -6.333
Ġconfusing;ĠangleĠBACĠisĠjustĠoneĠangleĠatĠvertexĠA,ĠbutĠperhapsĠinĠtermsĠofĠcoordinateĠgeometry,
Rollout 21, Act: -6.335
1},ĠwhichĠareĠsubsetsĠofĠZ,ĠnotĠsurjectiveĠontoĠZ.ĠSoĠSĠwouldĠnotĠbeĠaĠsubset
Rollout 21, Act: -6.336
ĠholdsĠforĠtheĠidentityĠfunctionĠisĠtrivial.ĠForĠsurjectiveĠfunctions,ĠinjectiveĠfunctions,ĠsinceĠ2f
Rollout 72, Act: -6.338
:ĊĊInĠaĠregularĠpentagon,ĠtheĠdiagonalĠoverĠsideĠisĠtheĠgoldenĠratioĠÏĨĠ=Ġ(1Ġ+Ġsqrt
Rollout 1, Act: -6.345
CompareĠtoĠtheĠaboveĠline:ĊĊFromĠtheĠsumĠofĠnorms,ĠweĠhave:ĊĊ-⣨xĠ+Ġx',
Rollout 21, Act: -6.372
.ĠButĠtoĠhaveĠimageĠexactlyĠZ,ĠtheĠsurjective.ĠIfĠaĠfunctionĠfĠsatisfiesĠf(xĠ-f
Rollout 46, Act: -6.417
ĠtoĠtheĠgradientĠofĠU?ĠButĠonlyĠinĠanĠinertialĠframeĠwouldĠtheĠaccelerationĠequalĠtheĠgradientĠofĠthe
Rollout 46, Act: -6.431
?ĠHowever,ĠthatĠwouldĠbeĠtheĠcaseĠinĠanĠinertialĠframe,ĠbutĠtheĠpresenceĠofĠtheĠcentrifugal
Rollout 46, Act: -6.432
ĊĊButĠtheseĠwouldĠcorrespondĠtoĠtheĠaccelerationĠinĠanĠinertialĠframeĠminusĠtheĠcentrifugalĠacceleration?ĠI'm
Rollout 46, Act: -6.495
,ĠwithoutĠconsideringĠtheĠrotatingĠframe,ĠsoĠassumingĠanĠinertialĠframeĠwhereĠUĠisĠtheĠconventionalĠgravitationalĠpotential,
Rollout 84, Act: -6.614
ĠandĠ"twiceĠasĠmuch"ĠareĠbothĠadverbialĠphrasesĠmodifyingĠtheĠverbsĠ"purchased"Ġand
UP_PROJ
Top 16 Positive Activations
Rollout 7, Act: 3.364
ĠĠ$47$Ġ.Ċ<|im_start|>assistantĊ<|im_start|>thinkĊAlright,ĠsoĠI'mĠtryingĠtoĠsolveĠthis
Rollout 44, Act: 3.314
mathrm{T}_{2}$Ċ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,ĠsoĠIĠneedĠtoĠfigureĠoutĠwhich
Rollout 26, Act: 3.305
mol}^{-1}$Ġ]Ċ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,Ġlet'sĠtryĠtoĠfigureĠthisĠproblem
Rollout 98, Act: 3.256
Ċ(D)Ġ2Ċ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,ĠsoĠIĠneedĠtoĠfigureĠoutĠhow
Rollout 6, Act: 3.238
$Ġ.ĠĠ[/*]Ċ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,ĠletĠmeĠtryĠtoĠworkĠthroughĠthese
Rollout 94, Act: 3.231
Ċ(D)Ġa,bĊ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,ĠsoĠIĠneedĠtoĠdetermineĠwhichĠof
Rollout 18, Act: 3.215
=H_{xy}$Ġ.Ċ<|im_start|>assistantĊ<|im_start|>thinkĊAlright,Ġlet'sĠtackleĠthisĠproblemĠstepĠby
Rollout 45, Act: 3.193
ĠofĠĠ$Ġm$Ġ.Ċ<|im_start|>assistantĊ<|im_start|>thinkĊAlright,ĠsoĠIĠhaveĠthisĠproblemĠwhereĠa
Rollout 36, Act: 3.189
Ġ.ĠFindĠ$AP.$Ċ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,ĠletĠmeĠtryĠtoĠfigureĠoutĠhow
Rollout 29, Act: 3.182
Ġ\rhoĠgH$ĠĊ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,ĠletĠmeĠtryĠtoĠfigureĠoutĠthis
Rollout 23, Act: 3.180
555ĠBqĊ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,Ġlet'sĠtackleĠthisĠproblemĠstepĠby
Rollout 79, Act: 3.179
ĠfacilityĠ(8,4)Ċ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,Ġlet'sĠtackleĠthisĠcrosswordĠclue.
Rollout 54, Act: 3.174
,ĠBĠ=Ġ2Ċ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,Ġlet'sĠtackleĠthisĠquestionĠstepĠby
Rollout 1, Act: 3.172
mathcal{H}$Ġ.Ċ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,ĠsoĠIĠneedĠtoĠshowĠthatĠthere
Rollout 11, Act: 3.169
Ġ.ĊĊ*DavidĠAltizio*Ċ<|im_start|>assistantĊ<|im_start|>thinkĊOkay,ĠsoĠIĠhaveĠthisĠproblemĠhereĠwhere
Rollout 55, Act: 3.157
018}.$Ċ<|im_start|>assistantĊ<|im_start|>thinkĊAlright,ĠsoĠIĠhaveĠthisĠmatrixĠAĠand
Top 16 Negative Activations
Rollout 22, Act: -2.270
T/m)ĊĊv_meanĠ=Ġsqrt(8kT/(ÏĢm))ĊĊAlright,ĠsoĠfirstĠIĠneed
Rollout 54, Act: -2.275
ideĠ(strongĠbase)ĊĊ5.ĠEthanethiolateĠ(weakerĠbaseĠthanĠhydroxide)ĊĊ3
Rollout 15, Act: -2.280
Ġ-ĠTheĠsystemĠcanĠbeĠrepresentedĠbyĠaĠtridiagonalĠmatrixĠ\(ĠMĠ\)ĠwhereĠeachĠrowĠhasĠ
Rollout 54, Act: -2.291
ĠisĠmostĠhydrated)Ċ-ĠRSâĪĴĠ(thiolate)ĠisĠaĠbetterĠnucleophileĠthanĠROâĪĴĠ(
Rollout 54, Act: -2.291
,ĠmethanolĠ(neutral),Ġethanethiolate.ĠPropionateĠisĠaĠcarboxylate,
Rollout 54, Act: -2.294
KaĠaroundĠ10,ĠethanethiolateĠ(R-SâĪĴ)ĠwouldĠhaveĠaĠbaseĠstrength
Rollout 54, Act: -2.302
ĠbaseĠ(strongestĠacid),ĠethanethiolateĠnextĠ(stillĠweakerĠbaseĠthanĠhydroxideĠand
Rollout 26, Act: -2.307
DeltaĠH_f^\circĠ(\mathrm{HgO})Ġ=Ġ\frac{-180.7
Rollout 97, Act: -2.315
ĠmayĠnotĠbeĠprecise.ĠBecauseĠtheĠreactionĠstoichiometryĠisĠmoles,ĠbutĠinĠtermsĠofĠpartialĠpressures
Rollout 54, Act: -2.340
Ġbases.ĊĊThus,ĠevenĠthoughĠethanethiolateĠ(5)ĠisĠaĠweakerĠbaseĠthanĠhydrox
Rollout 54, Act: -2.345
)Ġ>ĠhydroxideĠ>ĠethanethiolateĠ>ĠpropionateĠ(weakestĠbase).ĊĊThen,
Rollout 54, Act: -2.345
:ĊĊOrder:Ġ5Ġ(ethanethiolate)Ġ>Ġ2Ġ(hydroxide)Ġ>
Rollout 54, Act: -2.410
Ġsolution:ĊĊInĠSN2Ġreactions,ĠtheĠthiolateĠionĠ(e.g.,ĠSHâĪĴ)ĠisĠa
Rollout 22, Act: -2.426
Ġare:ĊĊv_rmsĠ=Ġsqrt(3kT/m)ĊĊv_meanĠ=Ġsqrt(8kT
Rollout 15, Act: -2.537
SuchĠmatricesĠareĠcalledĠJacobiĠmatricesĠorĠtridiagonalĠmatrices.ĠNilpotencyĠcanĠbeĠdiscussedĠviaĠtheir
Rollout 15, Act: -2.596
ĠpolynomialĠisĠx^n.ĊĊButĠforĠanyĠtridiagonalĠmatrix,ĠparticularlyĠsymmetricĠones,ĠeigenvaluesĠareĠreal
DOWN_PROJ
Top 16 Positive Activations
Rollout 79, Act: 2.599
Ġuse:ĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.588
ĠâĢĵĠlettersĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.533
Ġchanges":ĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.529
Ġchanges":ĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.476
Ġagain:ĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.465
"Ġ:ĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.461
Ġchanges":ĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.446
ĠlettersĠ(M,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.435
Ġletters:ĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.414
ĠlettersĠ(M,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.409
Ġletters:ĠM,ĠI,ĠN,ĠO,ĠR,ĠH,ĠN,ĠG.ĠLet'sĠsee
Rollout 79, Act: 2.395
Ġcheck:ĠM,ĠI,ĠN,ĠO,ĠRĠplusĠH,ĠG,ĠN.ĠThatĠcouldĠbe
Rollout 79, Act: 2.385
ĠhasĠlettersĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.375
Ġletters:ĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.373
ĠhaveĠareĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Rollout 79, Act: 2.336
)ĠareĠM,ĠI,ĠN,ĠO,ĠR,ĠC,ĠH,ĠA,ĠN,ĠG
Top 16 Negative Activations
Rollout 79, Act: -1.375
".ĊĊSoĠmaybeĠ"minorĠchanges"ĠisĠanĠanagramĠforĠtheĠanswer.ĠLet'sĠtryĠtoĠrearrange
Rollout 49, Act: -1.380
ĠunionĠofĠclosedĠsets)ĠisĠcalledĠaĠ"perfectlyĠnormal"Ġspace?ĠNotĠexactly.ĠPerfectlyĠnormal
Rollout 79, Act: -1.382
ĠanswerĠisĠ"somethingĠsomething"Ġthat'sĠanĠanagramĠofĠ"minorĠchanges"ĠplusĠsomeĠletters.ĠWait
Rollout 79, Act: -1.382
.ĠSoĠmaybeĠ"minorĠchanges"ĠisĠtheĠanagramĠfodder,ĠwhichĠwouldĠformĠanĠ8-letterĠword
Rollout 79, Act: -1.388
".ĠTheĠwordplayĠusuallyĠinvolvesĠsomeĠkindĠofĠanagram,Ġreversal,ĠhiddenĠword,Ġetc.Ġ"Not
Rollout 39, Act: -1.390
9...ĠpartĠbecomesĠ111...ĠandĠthenĠ7101ĠbecomesĠ789
Rollout 79, Act: -1.397
Ġagain.ĊĊIfĠ"Noticed"ĠisĠtheĠanagramĠindicator,ĠthenĠanagramĠofĠ"minorĠchangesĠin
Rollout 79, Act: -1.403
'sĠsee.ĠIfĠ"noticed"ĠisĠtheĠanagramĠindicator,ĠthenĠ"minorĠchanges"ĠhasĠtoĠbe
Rollout 51, Act: -1.424
ĠvariableĠtoĠyĠ=ĠxĠ-Ġθ,ĠandĠthenĠconsideringĠtheĠintegralĠfromĠ-θĠtoĠ2ÏĢ
Rollout 79, Act: -1.427
,ĠthenĠ"minorĠchanges"ĠhasĠtoĠbeĠanagrammed.ĠLet'sĠcheckĠtheĠletters.Ġ"Minor
Rollout 74, Act: -1.456
Ġfore-and-aftĠcomponentĠK_bĠ(proportionalĠtoĠtheĠEarth'sĠfield?)ĠandĠathwartships
Rollout 57, Act: -1.462
penĠsets.ĠWait,ĠperhapsĠregularityĠisĠaĠresultĠofĠtheĠdensityĠtopologyĠbeingĠaĠregularĠtopologyĠthroughĠits
Rollout 79, Act: -1.483
Ġetc.Ġ"Noticed"ĠmightĠbeĠtheĠanagramĠindicator.Ġ"MinorĠchanges"ĠcouldĠbeĠtheĠletters
Rollout 62, Act: -1.532
âĪĴm+11.](https://oeis.org/search?q=%22m%5E
Rollout 79, Act: -1.571
ĠwordsĠfromĠtheseĠlettersĠinclude:ĊĊ-Ġ"Hernias"ĠplusĠsomeĠothers.ĠNo.ĠMaybeĠ"Chair
Rollout 23, Act: -1.590
YouĠareĠaĠhelpfulĠmathematicsĠassistant.Ċ<|im_start|>userĊImagineĠaĠradioactiveĠnucleiĠX(Z,A)ĠcanĠdecayĠinto